MMA+Labwork+Day+4+Transformations

**Translations, Rotations, Reflections! **
 * Transformations with Geometer's Sketchpad **


 * Activity 1: Introduction to GSP and how to create a polygon **

 The tools names from top to bottom are.
 * GSP Tools and their uses: **There is a toolbar on the left side of the GSP window.
 * Selection Tool ** – allows selection of items on screen and is the default tool.
 * Point Tool ** – places points in the sketch at the place defined by the mouse position.
 * Circle Tool ** – draws circles in the sketch.
 * Straightedge Tool ** – allows the user to draw lines, segments, rays, etc.
 * Text Tool **<span style="font-family: Tahoma,sans-serif;"> – allows the user to make labels and add text to the screen.
 * <span style="font-family: Tahoma,sans-serif;">Custom Tool **<span style="font-family: Tahoma,sans-serif;"> – allows the user to create customized tools.

//<span style="font-family: Tahoma,sans-serif;">Time to Start: //<span style="font-family: Tahoma,sans-serif;"> Experiment with the tools by drawing some points, lines, rays, segments in the sketch. To change the segment tool into a line tool you must place the cursor the tool and right click on the mouse, holding the button on the mouse down you drag the cursor to the right and there will be segments, lines and rays. Once you have the cursor on your choice let go of the mouse button.

//<span style="font-family: Tahoma,sans-serif;">Selection or Highlighting //<span style="font-family: Tahoma,sans-serif;">: Click the Selection tool and then click on one of the points you created on the screen. Notice that the point is now colored pink. This signifies that the object is selected. If you click in the white space on the screen, notice the point is no longer pink. Experiment with the selection tool to answer the following questions.


 * //<span style="font-family: Tahoma,sans-serif;">1a) How to select one or more objects? //**
 * //<span style="font-family: Tahoma,sans-serif;">1b) How to deselect objects? //**
 * //<span style="font-family: Tahoma,sans-serif;">1c) How do you know when an object is selected? //**


 * __<span style="font-family: Tahoma,sans-serif;">Creating a polygon with points and menus __**

<span style="font-family: Tahoma,sans-serif;">Close your sketch, but do not save your experimental work. Open a blank sketch by choosing the **File** menu and selecting **“New Sketch”**. Now we need to set up our coordinate system. Choose the **Graph** menu and select **“Show Grid”**. Next choose **“Snap Points”** also in the **Graph** menu. See the figures below for clarification. See the samples below to view the menus as they should appear.

<span style="font-family: Tahoma,sans-serif;"> <span style="font-family: Tahoma,sans-serif;"> “Show Grid” “Snap Points”

<span style="font-family: Tahoma,sans-serif;">In this new sketch we will create a polygon.
 * <span style="font-family: Tahoma,sans-serif;">Select the point tool
 * <span style="font-family: Tahoma,sans-serif;">Holding the shift key, place three (3) points in either clockwise or counter clockwise order.
 * <span style="font-family: Tahoma,sans-serif;">With all three (3) points selected in order, go to the **Construct** menu and select **“segments”**

<span style="font-family: Tahoma,sans-serif;">You have now created a triangle. Select the **Text Tool** and click on each of the triangle’s vertices (points). We now have names for the vertices (points). You can double click on the label and type in the box to rename your points if they do not match the facilitator’s labels.

<span style="font-family: Tahoma,sans-serif;"> <span style="font-family: Tahoma,sans-serif;">Choose the **Selection Tool**. Click on one of the points to see how the triangle changes as each point is moved

<span style="font-family: Tahoma,sans-serif;">Now use the points/segments method to create a square, a rectangle and a pentagon in your sketch.

<span style="font-family: Tahoma,sans-serif;">Now that we can create and move a triangle using GSP, we will discover the other ways we can change our triangle. We will use the GSP functions from the Transform menu.
 * __<span style="font-family: Tahoma,sans-serif;">Activity 2: Translation, dilation, reflection and rotation of a triangle __**

<span style="font-family: Tahoma,sans-serif;">Translation is determined by moving an object a given distance in a given direction. In this portion of the activity we will learn one method that is used to perform translations using GSP.
 * <span style="font-family: Tahoma,sans-serif;">Translation **


 * 1) <span style="font-family: Tahoma,sans-serif;">Create a new sketch and create a new triangle as we did in Activity. Make sure to label the points.
 * 2) <span style="font-family: Tahoma,sans-serif;">Select the triangle by choosing the selection tool and making a box around the whole triangle.
 * 3) <span style="font-family: Tahoma,sans-serif;">Go to the Transform menu and select “Translate…”

<span style="font-family: Tahoma,sans-serif;">


 * 1) <span style="font-family: Tahoma,sans-serif;">A dialog box will appear on the screen. Set the Translation Vector to “Rectangular”. Next, change the Horizontal distance to 10.0 cm and the Vertical distance to 0. See the figure below for clarification

<span style="font-family: Tahoma,sans-serif;">


 * //<span style="font-family: Tahoma,sans-serif;">2a) What happened to the triangle? //**
 * //<span style="font-family: Tahoma,sans-serif;">2b) What happened to each point of the triangle with regards to each point’s coordinates? //**

<span style="font-family: Tahoma,sans-serif;">Select your original triangle and perform another translation. This time, make the Horizontal distance 0.0 cm and the Vertical Distance -4.0 cm.


 * //<span style="font-family: Tahoma,sans-serif;">2c) What happened to the triangle after this translation? //**
 * //<span style="font-family: Tahoma,sans-serif;">2d) What happened to the coordinates of the vertices of the triangle? //**

<span style="font-family: Tahoma,sans-serif;">Repeat the translation process a few times with different values to determine the values that make the triangle move up, down, right and left. Record your observations below.


 * //<span style="font-family: Tahoma,sans-serif;">3a) Describe the type of values that made the triangle move Up- //**
 * //<span style="font-family: Tahoma,sans-serif;">3b) Describe the type of values that made the triangle move Down- //**
 * //<span style="font-family: Tahoma,sans-serif;">3c) Describe the type of values that made the triangle move Left – //**
 * //<span style="font-family: Tahoma,sans-serif;">3d) Describe the type of values that made the triangle move Right – //**

<span style="font-family: Tahoma,sans-serif;">When a point or object is reflected, it must have a reference point and a line to reflect the object over. A reflection is similar to looking in a mirror or into still water. The mirror reflection is similar in nature to the image you obtain after performing a reflection. The following activity covers how to reflect objects using GSP.
 * __<span style="font-family: Tahoma,sans-serif;">Reflection __**


 * 1) <span style="font-family: Tahoma,sans-serif;">Using the method from Activity 1, create a new sketch and create a new triangle. Make sure to label the points.
 * 2) <span style="font-family: Tahoma,sans-serif;">Highlight the y-axis (vertical) by clicking it.
 * 3) <span style="font-family: Tahoma,sans-serif;">Go to the **Transform** menu and select **“Mark Mirror”**
 * 4) <span style="font-family: Tahoma,sans-serif;">Select the triangle by choosing the selection tool and making a box around the whole triangle.
 * 5) <span style="font-family: Tahoma,sans-serif;">Go to the **Transform** menu and select **“Reflect”**.
 * 6) <span style="font-family: Tahoma,sans-serif;">Use the Text Tool to label the points of the new triangle.


 * //<span style="font-family: Tahoma,sans-serif;">4a) What happened to the triangle? Did it change size or shape? //**
 * //<span style="font-family: Tahoma,sans-serif;">4b) How did the coordinates of each point change? //**
 * //<span style="font-family: Tahoma,sans-serif;">4c) What did GSP label the vertices of the image? //**

<span style="font-family: Tahoma,sans-serif;">Explore reflections further by repeating the steps above. Instead of selecting the y-axis for the mirror, try the using the following as a line of reflection one at a time of course and record what happens:


 * //<span style="font-family: Tahoma,sans-serif;">5a) Describe what happens when you perform the reflection using the X-axis: //**
 * //<span style="font-family: Tahoma,sans-serif;">5b) Describe what happens when you perform the reflection using a point for the mirror: //**
 * //<span style="font-family: Tahoma,sans-serif;">5c) Describe what happens when you perform the reflection using an edge for the mirror: //**
 * //<span style="font-family: Tahoma,sans-serif;">5d) Describe what happens when you perform the reflection using any line: //**

<span style="font-family: Tahoma,sans-serif;">Another method of moving an object is rotation. In rotation, a point or object is moved about a fixed point, clockwise or counter clockwise a fixed number of degrees. The center of the rotation is determined by the user in GSP. This activity will demonstrate one method to execute rotation of our triangle using GSP.
 * __<span style="font-family: Tahoma,sans-serif;">Rotation __**

<span style="font-family: Tahoma,sans-serif;">
 * 1) <span style="font-family: Tahoma,sans-serif;">Create a new sketch and create a new triangle (use the method from Activity 1.) Be sure to label the points.
 * 2) <span style="font-family: Tahoma,sans-serif;">Highlight (select) the origin of the graph (x = 0, y = 0)
 * 3) <span style="font-family: Tahoma,sans-serif;">Go to the **Transform** menu and select **“Mark Center”.**


 * 1) <span style="font-family: Tahoma,sans-serif;">We have now selected the point about which we will rotate our triangle.
 * 2) <span style="font-family: Tahoma,sans-serif;">To rotate the triangle, highlight the triangle and then go to the **Transform** menu and select **“Rotate…”**.
 * 3) <span style="font-family: Tahoma,sans-serif;">The dialog box shown below will appear on the screen. The default angle is 90o. We will use the default value for our first rotation. Select **“Rotate”** to complete the rotation.

<span style="font-family: Tahoma,sans-serif;">


 * //<span style="font-family: Tahoma,sans-serif;">6a) What happened to the triangle? //**
 * //<span style="font-family: Tahoma,sans-serif;">6b) What quadrant is the rotated triangle in? //**
 * //<span style="font-family: Tahoma,sans-serif;">6c) What quadrant is the original triangle in? //**
 * //<span style="font-family: Tahoma,sans-serif;">6d)What happens if you rotate the image of your first rotation (that is rotate the second triangle) by 90o? //**
 * //<span style="font-family: Tahoma,sans-serif;">6e)What quadrant is the triangle located? //**
 * //<span style="font-family: Tahoma,sans-serif;">6f) What happens to the third triangle if you rotate it by another 90o? //**
 * //<span style="font-family: Tahoma,sans-serif;">6g) What quadrant is the triangle located? //**

<span style="font-family: Tahoma,sans-serif;">Now pick a one of the vertices of the triangle to mark as your center. Rotate the triangle 90o degrees.


 * //<span style="font-family: Tahoma,sans-serif;">7a) Describe how the image in a 90o differs with the new center you chose. //**

<span style="font-family: Tahoma,sans-serif;">Experiment with the rotation function by using different rotation angles and different points as the center of rotation. <span style="font-family: Tahoma,sans-serif;">Rotation and translation are called transformations since they transform an object.